LMFDB - Embedded newform 805.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(1,805)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$6.42795736271$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.255877.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 6x^{2} + 6x - 5 $ x^5 - x^4 - 6x^3 + 6x^2 + 6*x - 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.06459$ of defining polynomial
Character	$\chi$	$=$	805.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06459 q^{2} +0.382286 q^{3} -0.866643 q^{4} -1.00000 q^{5} +0.406979 q^{6} +1.00000 q^{7} -3.05181 q^{8} -2.85386 q^{9} +O(q^{10})$	\(q+1.06459 q^{2} +0.382286 q^{3} -0.866643 q^{4} -1.00000 q^{5} +0.406979 q^{6} +1.00000 q^{7} -3.05181 q^{8} -2.85386 q^{9} -1.06459 q^{10} +0.351000 q^{11} -0.331306 q^{12} -1.26172 q^{13} +1.06459 q^{14} -0.382286 q^{15} -1.51564 q^{16} -4.54276 q^{17} -3.03819 q^{18} -3.54895 q^{19} +0.866643 q^{20} +0.382286 q^{21} +0.373672 q^{22} +1.00000 q^{23} -1.16666 q^{24} +1.00000 q^{25} -1.34321 q^{26} -2.23785 q^{27} -0.866643 q^{28} -7.79870 q^{29} -0.406979 q^{30} +1.85386 q^{31} +4.49007 q^{32} +0.134183 q^{33} -4.83618 q^{34} -1.00000 q^{35} +2.47328 q^{36} -7.24476 q^{37} -3.77818 q^{38} -0.482336 q^{39} +3.05181 q^{40} +1.37033 q^{41} +0.406979 q^{42} +2.84195 q^{43} -0.304192 q^{44} +2.85386 q^{45} +1.06459 q^{46} -0.960100 q^{47} -0.579409 q^{48} +1.00000 q^{49} +1.06459 q^{50} -1.73663 q^{51} +1.09346 q^{52} -5.48925 q^{53} -2.38240 q^{54} -0.351000 q^{55} -3.05181 q^{56} -1.35671 q^{57} -8.30244 q^{58} +3.30156 q^{59} +0.331306 q^{60} +4.14351 q^{61} +1.97360 q^{62} -2.85386 q^{63} +7.81138 q^{64} +1.26172 q^{65} +0.142850 q^{66} +8.46038 q^{67} +3.93695 q^{68} +0.382286 q^{69} -1.06459 q^{70} +3.58714 q^{71} +8.70942 q^{72} -2.45676 q^{73} -7.71271 q^{74} +0.382286 q^{75} +3.07567 q^{76} +0.351000 q^{77} -0.513492 q^{78} -3.96943 q^{79} +1.51564 q^{80} +7.70607 q^{81} +1.45884 q^{82} -11.5057 q^{83} -0.331306 q^{84} +4.54276 q^{85} +3.02552 q^{86} -2.98134 q^{87} -1.07119 q^{88} -3.82592 q^{89} +3.03819 q^{90} -1.26172 q^{91} -0.866643 q^{92} +0.708704 q^{93} -1.02212 q^{94} +3.54895 q^{95} +1.71649 q^{96} -15.6413 q^{97} +1.06459 q^{98} -1.00171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} + q^{10} - 7 q^{11} - 10 q^{12} - 5 q^{13} - q^{14} + 4 q^{15} - 9 q^{16} - 7 q^{17} + 11 q^{18} - 10 q^{19} - 3 q^{20} - 4 q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} + 5 q^{25} - 2 q^{26} - 7 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 10 q^{31} + 4 q^{33} - 10 q^{34} - 5 q^{35} + 20 q^{36} - 3 q^{37} - 15 q^{38} - 13 q^{39} - 3 q^{40} - 15 q^{41} - 5 q^{42} + 8 q^{43} - 27 q^{44} - 5 q^{45} - q^{46} - 10 q^{47} - 2 q^{48} + 5 q^{49} - q^{50} - 18 q^{51} + 18 q^{52} - 9 q^{53} - 39 q^{54} + 7 q^{55} + 3 q^{56} + 23 q^{57} - 31 q^{58} - 19 q^{59} + 10 q^{60} - 21 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} + 5 q^{65} + 25 q^{66} + 5 q^{67} - 15 q^{68} - 4 q^{69} + q^{70} - 16 q^{71} + 26 q^{72} + q^{73} - 16 q^{74} - 4 q^{75} - 7 q^{77} + 28 q^{78} + 20 q^{79} + 9 q^{80} - 3 q^{81} + 11 q^{82} - 31 q^{83} - 10 q^{84} + 7 q^{85} + 10 q^{86} + 38 q^{87} - 3 q^{88} - 21 q^{89} - 11 q^{90} - 5 q^{91} + 3 q^{92} + 23 q^{93} + 28 q^{94} + 10 q^{95} + 24 q^{96} + 19 q^{97} - q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 + q^10 - 7 * q^11 - 10 * q^12 - 5 * q^13 - q^14 + 4 * q^15 - 9 * q^16 - 7 * q^17 + 11 * q^18 - 10 * q^19 - 3 * q^20 - 4 * q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 + 5 * q^25 - 2 * q^26 - 7 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 10 * q^31 + 4 * q^33 - 10 * q^34 - 5 * q^35 + 20 * q^36 - 3 * q^37 - 15 * q^38 - 13 * q^39 - 3 * q^40 - 15 * q^41 - 5 * q^42 + 8 * q^43 - 27 * q^44 - 5 * q^45 - q^46 - 10 * q^47 - 2 * q^48 + 5 * q^49 - q^50 - 18 * q^51 + 18 * q^52 - 9 * q^53 - 39 * q^54 + 7 * q^55 + 3 * q^56 + 23 * q^57 - 31 * q^58 - 19 * q^59 + 10 * q^60 - 21 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 + 5 * q^65 + 25 * q^66 + 5 * q^67 - 15 * q^68 - 4 * q^69 + q^70 - 16 * q^71 + 26 * q^72 + q^73 - 16 * q^74 - 4 * q^75 - 7 * q^77 + 28 * q^78 + 20 * q^79 + 9 * q^80 - 3 * q^81 + 11 * q^82 - 31 * q^83 - 10 * q^84 + 7 * q^85 + 10 * q^86 + 38 * q^87 - 3 * q^88 - 21 * q^89 - 11 * q^90 - 5 * q^91 + 3 * q^92 + 23 * q^93 + 28 * q^94 + 10 * q^95 + 24 * q^96 + 19 * q^97 - q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.06459	0.752780	0.376390	−	0.926461i	$-0.377165\pi$
$2$	1.06459	0.752780	0.376390	+	0.926461i	$0.377165\pi$
$3$	0.382286	0.220713	0.110357	−	0.993892i	$-0.464801\pi$
$3$	0.382286	0.220713	0.110357	+	0.993892i	$0.464801\pi$
$4$	−0.866643	−0.433322
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.406979	0.166148
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.05181	−1.07898
$9$	−2.85386	−0.951286
$10$	−1.06459	−0.336654
$11$	0.351000	0.105831	0.0529153	−	0.998599i	$-0.483149\pi$
$11$	0.351000	0.105831	0.0529153	+	0.998599i	$0.483149\pi$
$12$	−0.331306	−0.0956397
$13$	−1.26172	−0.349937	−0.174968	−	0.984574i	$-0.555982\pi$
$13$	−1.26172	−0.349937	−0.174968	+	0.984574i	$0.555982\pi$
$14$	1.06459	0.284524
$15$	−0.382286	−0.0987059
$16$	−1.51564	−0.378911
$17$	−4.54276	−1.10178	−0.550890	−	0.834578i	$-0.685712\pi$
$17$	−4.54276	−1.10178	−0.550890	+	0.834578i	$0.685712\pi$
$18$	−3.03819	−0.716109
$19$	−3.54895	−0.814185	−0.407092	−	0.913387i	$-0.633457\pi$
$19$	−3.54895	−0.814185	−0.407092	+	0.913387i	$0.633457\pi$
$20$	0.866643	0.193787
$21$	0.382286	0.0834217
$22$	0.373672	0.0796672
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.16666	−0.238144
$25$	1.00000	0.200000
$26$	−1.34321	−0.263426
$27$	−2.23785	−0.430674
$28$	−0.866643	−0.163780
$29$	−7.79870	−1.44818	−0.724092	−	0.689704i	$-0.757741\pi$
$29$	−7.79870	−1.44818	−0.724092	+	0.689704i	$0.757741\pi$
$30$	−0.406979	−0.0743038
$31$	1.85386	0.332963	0.166481	−	0.986045i	$-0.446759\pi$
$31$	1.85386	0.332963	0.166481	+	0.986045i	$0.446759\pi$
$32$	4.49007	0.793740
$33$	0.134183	0.0233582
$34$	−4.83618	−0.829399
$35$	−1.00000	−0.169031
$36$	2.47328	0.412213
$37$	−7.24476	−1.19103	−0.595515	−	0.803344i	$-0.703052\pi$
$37$	−7.24476	−1.19103	−0.595515	+	0.803344i	$0.703052\pi$
$38$	−3.77818	−0.612902
$39$	−0.482336	−0.0772356
$40$	3.05181	0.482533
$41$	1.37033	0.214009	0.107004	−	0.994259i	$-0.465874\pi$
$41$	1.37033	0.214009	0.107004	+	0.994259i	$0.465874\pi$
$42$	0.406979	0.0627982
$43$	2.84195	0.433393	0.216697	−	0.976239i	$-0.430472\pi$
$43$	2.84195	0.433393	0.216697	+	0.976239i	$0.430472\pi$
$44$	−0.304192	−0.0458587
$45$	2.85386	0.425428
$46$	1.06459	0.156966
$47$	−0.960100	−0.140045	−0.0700225	−	0.997545i	$-0.522307\pi$
$47$	−0.960100	−0.140045	−0.0700225	+	0.997545i	$0.522307\pi$
$48$	−0.579409	−0.0836305
$49$	1.00000	0.142857
$50$	1.06459	0.150556
$51$	−1.73663	−0.243177
$52$	1.09346	0.151635
$53$	−5.48925	−0.754006	−0.377003	−	0.926212i	$-0.623045\pi$
$53$	−5.48925	−0.754006	−0.377003	+	0.926212i	$0.623045\pi$
$54$	−2.38240	−0.324203
$55$	−0.351000	−0.0473289
$56$	−3.05181	−0.407815
$57$	−1.35671	−0.179701
$58$	−8.30244	−1.09016
$59$	3.30156	0.429827	0.214913	−	0.976633i	$-0.431053\pi$
$59$	3.30156	0.429827	0.214913	+	0.976633i	$0.431053\pi$
$60$	0.331306	0.0427714
$61$	4.14351	0.530522	0.265261	−	0.964177i	$-0.414542\pi$
$61$	4.14351	0.530522	0.265261	+	0.964177i	$0.414542\pi$
$62$	1.97360	0.250648
$63$	−2.85386	−0.359552
$64$	7.81138	0.976423
$65$	1.26172	0.156497
$66$	0.142850	0.0175836
$67$	8.46038	1.03360	0.516800	−	0.856106i	$-0.327123\pi$
$67$	8.46038	1.03360	0.516800	+	0.856106i	$0.327123\pi$
$68$	3.93695	0.477425
$69$	0.382286	0.0460218
$70$	−1.06459	−0.127243
$71$	3.58714	0.425716	0.212858	−	0.977083i	$-0.431723\pi$
$71$	3.58714	0.425716	0.212858	+	0.977083i	$0.431723\pi$
$72$	8.70942	1.02641
$73$	−2.45676	−0.287543	−0.143771	−	0.989611i	$-0.545923\pi$
$73$	−2.45676	−0.287543	−0.143771	+	0.989611i	$0.545923\pi$
$74$	−7.71271	−0.896585
$75$	0.382286	0.0441426
$76$	3.07567	0.352804
$77$	0.351000	0.0400002
$78$	−0.513492	−0.0581415
$79$	−3.96943	−0.446596	−0.223298	−	0.974750i	$-0.571682\pi$
$79$	−3.96943	−0.446596	−0.223298	+	0.974750i	$0.571682\pi$
$80$	1.51564	0.169454
$81$	7.70607	0.856230
$82$	1.45884	0.161102
$83$	−11.5057	−1.26292	−0.631458	−	0.775410i	$-0.717543\pi$
$83$	−11.5057	−1.26292	−0.631458	+	0.775410i	$0.717543\pi$
$84$	−0.331306	−0.0361484
$85$	4.54276	0.492731
$86$	3.02552	0.326250
$87$	−2.98134	−0.319633
$88$	−1.07119	−0.114189
$89$	−3.82592	−0.405546	−0.202773	−	0.979226i	$-0.564995\pi$
$89$	−3.82592	−0.405546	−0.202773	+	0.979226i	$0.564995\pi$
$90$	3.03819	0.320254
$91$	−1.26172	−0.132264
$92$	−0.866643	−0.0903538
$93$	0.708704	0.0734892
$94$	−1.02212	−0.105423
$95$	3.54895	0.364115
$96$	1.71649	0.175189
$97$	−15.6413	−1.58814	−0.794068	−	0.607829i	$-0.792040\pi$
$97$	−15.6413	−1.58814	−0.794068	+	0.607829i	$0.792040\pi$
$98$	1.06459	0.107540
$99$	−1.00171	−0.100675
$100$	−0.866643	−0.0866643
$101$	−6.61723	−0.658439	−0.329220	−	0.944253i	$-0.606786\pi$
$101$	−6.61723	−0.658439	−0.329220	+	0.944253i	$0.606786\pi$
$102$	−1.84881	−0.183059
$103$	10.6612	1.05048	0.525238	−	0.850955i	$-0.323976\pi$
$103$	10.6612	1.05048	0.525238	+	0.850955i	$0.323976\pi$
$104$	3.85051	0.377574
$105$	−0.382286	−0.0373073
$106$	−5.84381	−0.567601
$107$	10.5690	1.02174	0.510871	−	0.859657i	$-0.329323\pi$
$107$	10.5690	1.02174	0.510871	+	0.859657i	$0.329323\pi$
$108$	1.93942	0.186620
$109$	19.3928	1.85749	0.928745	−	0.370720i	$-0.120889\pi$
$109$	19.3928	1.85749	0.928745	+	0.370720i	$0.120889\pi$
$110$	−0.373672	−0.0356283
$111$	−2.76957	−0.262876
$112$	−1.51564	−0.143215
$113$	11.7220	1.10272	0.551358	−	0.834268i	$-0.314110\pi$
$113$	11.7220	1.10272	0.551358	+	0.834268i	$0.314110\pi$
$114$	−1.44435	−0.135276
$115$	−1.00000	−0.0932505
$116$	6.75870	0.627529
$117$	3.60076	0.332890
$118$	3.51482	0.323565
$119$	−4.54276	−0.416434
$120$	1.16666	0.106501
$121$	−10.8768	−0.988800
$122$	4.41115	0.399367
$123$	0.523857	0.0472346
$124$	−1.60663	−0.144280
$125$	−1.00000	−0.0894427
$126$	−3.03819	−0.270664
$127$	15.9575	1.41600	0.707998	−	0.706214i	$-0.249598\pi$
$127$	15.9575	1.41600	0.707998	+	0.706214i	$0.249598\pi$
$128$	−0.664206	−0.0587081
$129$	1.08644	0.0956556
$130$	1.34321	0.117808
$131$	−11.7189	−1.02389	−0.511943	−	0.859020i	$-0.671074\pi$
$131$	−11.7189	−1.02389	−0.511943	+	0.859020i	$0.671074\pi$
$132$	−0.116288	−0.0101216
$133$	−3.54895	−0.307733
$134$	9.00686	0.778074
$135$	2.23785	0.192603
$136$	13.8636	1.18879
$137$	14.0086	1.19683	0.598416	−	0.801186i	$-0.295797\pi$
$137$	14.0086	1.19683	0.598416	+	0.801186i	$0.295797\pi$
$138$	0.406979	0.0346443
$139$	−8.17686	−0.693553	−0.346776	−	0.937948i	$-0.612724\pi$
$139$	−8.17686	−0.693553	−0.346776	+	0.937948i	$0.612724\pi$
$140$	0.866643	0.0732447
$141$	−0.367033	−0.0309098
$142$	3.81885	0.320470
$143$	−0.442863	−0.0370340
$144$	4.32543	0.360452
$145$	7.79870	0.647647
$146$	−2.61545	−0.216456
$147$	0.382286	0.0315304
$148$	6.27862	0.516099
$149$	−10.5212	−0.861932	−0.430966	−	0.902368i	$-0.641827\pi$
$149$	−10.5212	−0.861932	−0.430966	+	0.902368i	$0.641827\pi$
$150$	0.406979	0.0332297
$151$	20.7280	1.68682	0.843411	−	0.537268i	$-0.180544\pi$
$151$	20.7280	1.68682	0.843411	+	0.537268i	$0.180544\pi$
$152$	10.8307	0.878486
$153$	12.9644	1.04811
$154$	0.373672	0.0301114
$155$	−1.85386	−0.148905
$156$	0.418014	0.0334679
$157$	−4.03604	−0.322111	−0.161056	−	0.986945i	$-0.551490\pi$
$157$	−4.03604	−0.322111	−0.161056	+	0.986945i	$0.551490\pi$
$158$	−4.22582	−0.336189
$159$	−2.09846	−0.166419
$160$	−4.49007	−0.354971
$161$	1.00000	0.0788110
$162$	8.20383	0.644553
$163$	−10.6497	−0.834146	−0.417073	−	0.908873i	$-0.636944\pi$
$163$	−10.6497	−0.834146	−0.417073	+	0.908873i	$0.636944\pi$
$164$	−1.18758	−0.0927347
$165$	−0.134183	−0.0104461
$166$	−12.2489	−0.950698
$167$	−21.0857	−1.63166	−0.815831	−	0.578290i	$-0.803720\pi$
$167$	−21.0857	−1.63166	−0.815831	+	0.578290i	$0.803720\pi$
$168$	−1.16666	−0.0900100
$169$	−11.4081	−0.877544
$170$	4.83618	0.370918
$171$	10.1282	0.774522
$172$	−2.46296	−0.187799
$173$	−11.7526	−0.893535	−0.446767	−	0.894650i	$-0.647425\pi$
$173$	−11.7526	−0.893535	−0.446767	+	0.894650i	$0.647425\pi$
$174$	−3.17391	−0.240613
$175$	1.00000	0.0755929
$176$	−0.531991	−0.0401004
$177$	1.26214	0.0948683
$178$	−4.07304	−0.305287
$179$	0.898702	0.0671721	0.0335861	−	0.999436i	$-0.489307\pi$
$179$	0.898702	0.0671721	0.0335861	+	0.999436i	$0.489307\pi$
$180$	−2.47328	−0.184347
$181$	−19.3459	−1.43797	−0.718987	−	0.695024i	$-0.755394\pi$
$181$	−19.3459	−1.43797	−0.718987	+	0.695024i	$0.755394\pi$
$182$	−1.34321	−0.0995655
$183$	1.58401	0.117093
$184$	−3.05181	−0.224982
$185$	7.24476	0.532645
$186$	0.754481	0.0553212
$187$	−1.59451	−0.116602
$188$	0.832065	0.0606845
$189$	−2.23785	−0.162780
$190$	3.77818	0.274098
$191$	−9.30156	−0.673037	−0.336519	−	0.941677i	$-0.609250\pi$
$191$	−9.30156	−0.673037	−0.336519	+	0.941677i	$0.609250\pi$
$192$	2.98618	0.215509
$193$	−2.03033	−0.146146	−0.0730732	−	0.997327i	$-0.523281\pi$
$193$	−2.03033	−0.146146	−0.0730732	+	0.997327i	$0.523281\pi$
$194$	−16.6516	−1.19552
$195$	0.482336	0.0345408
$196$	−0.866643	−0.0619031
$197$	13.9377	0.993020	0.496510	−	0.868031i	$-0.334615\pi$
$197$	13.9377	0.993020	0.496510	+	0.868031i	$0.334615\pi$
$198$	−1.06641	−0.0757863
$199$	−8.99450	−0.637603	−0.318802	−	0.947821i	$-0.603280\pi$
$199$	−8.99450	−0.637603	−0.318802	+	0.947821i	$0.603280\pi$
$200$	−3.05181	−0.215795
$201$	3.23429	0.228129
$202$	−7.04466	−0.495660
$203$	−7.79870	−0.547362
$204$	1.50504	0.105374
$205$	−1.37033	−0.0957077
$206$	11.3498	0.790778
$207$	−2.85386	−0.198357
$208$	1.91231	0.132595
$209$	−1.24568	−0.0861657
$210$	−0.406979	−0.0280842
$211$	−0.881850	−0.0607091	−0.0303545	−	0.999539i	$-0.509664\pi$
$211$	−0.881850	−0.0607091	−0.0303545	+	0.999539i	$0.509664\pi$
$212$	4.75722	0.326727
$213$	1.37132	0.0939610
$214$	11.2517	0.769148
$215$	−2.84195	−0.193819
$216$	6.82948	0.464687
$217$	1.85386	0.125848
$218$	20.6454	1.39828
$219$	−0.939187	−0.0634644
$220$	0.304192	0.0205086
$221$	5.73167	0.385554
$222$	−2.94846	−0.197888
$223$	−5.70243	−0.381863	−0.190931	−	0.981603i	$-0.561151\pi$
$223$	−5.70243	−0.381863	−0.190931	+	0.981603i	$0.561151\pi$
$224$	4.49007	0.300005
$225$	−2.85386	−0.190257
$226$	12.4792	0.830104
$227$	8.54919	0.567429	0.283715	−	0.958909i	$-0.408433\pi$
$227$	8.54919	0.567429	0.283715	+	0.958909i	$0.408433\pi$
$228$	1.17579	0.0778684
$229$	−13.8393	−0.914528	−0.457264	−	0.889331i	$-0.651171\pi$
$229$	−13.8393	−0.914528	−0.457264	+	0.889331i	$0.651171\pi$
$230$	−1.06459	−0.0701971
$231$	0.134183	0.00882857
$232$	23.8001	1.56256
$233$	−1.64236	−0.107595	−0.0537973	−	0.998552i	$-0.517132\pi$
$233$	−1.64236	−0.107595	−0.0537973	+	0.998552i	$0.517132\pi$
$234$	3.83334	0.250593
$235$	0.960100	0.0626300
$236$	−2.86128	−0.186253
$237$	−1.51746	−0.0985695
$238$	−4.83618	−0.313483
$239$	−17.1611	−1.11006	−0.555029	−	0.831831i	$-0.687293\pi$
$239$	−17.1611	−1.11006	−0.555029	+	0.831831i	$0.687293\pi$
$240$	0.579409	0.0374007
$241$	19.4718	1.25429	0.627144	−	0.778903i	$-0.284224\pi$
$241$	19.4718	1.25429	0.627144	+	0.778903i	$0.284224\pi$
$242$	−11.5794	−0.744349
$243$	9.65947	0.619655
$244$	−3.59095	−0.229887
$245$	−1.00000	−0.0638877
$246$	0.557694	0.0355573
$247$	4.47776	0.284913
$248$	−5.65761	−0.359259
$249$	−4.39847	−0.278742
$250$	−1.06459	−0.0673307
$251$	1.85622	0.117164	0.0585819	−	0.998283i	$-0.481342\pi$
$251$	1.85622	0.117164	0.0585819	+	0.998283i	$0.481342\pi$
$252$	2.47328	0.155802
$253$	0.351000	0.0220672
$254$	16.9882	1.06593
$255$	1.73663	0.108752
$256$	−16.3299	−1.02062
$257$	14.2471	0.888708	0.444354	−	0.895851i	$-0.353433\pi$
$257$	14.2471	0.888708	0.444354	+	0.895851i	$0.353433\pi$
$258$	1.15661	0.0720076
$259$	−7.24476	−0.450167
$260$	−1.09346	−0.0678133
$261$	22.2564	1.37764
$262$	−12.4759	−0.770761
$263$	−6.98304	−0.430593	−0.215296	−	0.976549i	$-0.569072\pi$
$263$	−6.98304	−0.430593	−0.215296	+	0.976549i	$0.569072\pi$
$264$	−0.409499	−0.0252029
$265$	5.48925	0.337202
$266$	−3.77818	−0.231655
$267$	−1.46260	−0.0895094
$268$	−7.33213	−0.447881
$269$	−8.52176	−0.519581	−0.259790	−	0.965665i	$-0.583653\pi$
$269$	−8.52176	−0.519581	−0.259790	+	0.965665i	$0.583653\pi$
$270$	2.38240	0.144988
$271$	−15.7657	−0.957696	−0.478848	−	0.877898i	$-0.658945\pi$
$271$	−15.7657	−0.957696	−0.478848	+	0.877898i	$0.658945\pi$
$272$	6.88520	0.417476
$273$	−0.482336	−0.0291923
$274$	14.9134	0.900952
$275$	0.351000	0.0211661
$276$	−0.331306	−0.0199423
$277$	5.22949	0.314210	0.157105	−	0.987582i	$-0.449784\pi$
$277$	5.22949	0.314210	0.157105	+	0.987582i	$0.449784\pi$
$278$	−8.70503	−0.522093
$279$	−5.29064	−0.316743
$280$	3.05181	0.182380
$281$	−14.2138	−0.847922	−0.423961	−	0.905680i	$-0.639361\pi$
$281$	−14.2138	−0.847922	−0.423961	+	0.905680i	$0.639361\pi$
$282$	−0.390741	−0.0232683
$283$	18.8845	1.12257	0.561283	−	0.827624i	$-0.310308\pi$
$283$	18.8845	1.12257	0.561283	+	0.827624i	$0.310308\pi$
$284$	−3.10877	−0.184472
$285$	1.35671	0.0803648
$286$	−0.471468	−0.0278785
$287$	1.37033	0.0808878
$288$	−12.8140	−0.755073
$289$	3.63664	0.213920
$290$	8.30244	0.487536
$291$	−5.97946	−0.350522
$292$	2.12914	0.124598
$293$	20.0931	1.17385	0.586927	−	0.809640i	$-0.300338\pi$
$293$	20.0931	1.17385	0.586927	+	0.809640i	$0.300338\pi$
$294$	0.406979	0.0237355
$295$	−3.30156	−0.192224
$296$	22.1096	1.28509
$297$	−0.785486	−0.0455785
$298$	−11.2008	−0.648846
$299$	−1.26172	−0.0729669
$300$	−0.331306	−0.0191279
$301$	2.84195	0.163807
$302$	22.0669	1.26981
$303$	−2.52968	−0.145326
$304$	5.37894	0.308503
$305$	−4.14351	−0.237257
$306$	13.8018	0.788995
$307$	−3.30116	−0.188407	−0.0942035	−	0.995553i	$-0.530030\pi$
$307$	−3.30116	−0.188407	−0.0942035	+	0.995553i	$0.530030\pi$
$308$	−0.304192	−0.0173330
$309$	4.07562	0.231854
$310$	−1.97360	−0.112093
$311$	−28.7179	−1.62844	−0.814222	−	0.580553i	$-0.802836\pi$
$311$	−28.7179	−1.62844	−0.814222	+	0.580553i	$0.802836\pi$
$312$	1.47200	0.0833354
$313$	24.7834	1.40084	0.700420	−	0.713731i	$-0.252996\pi$
$313$	24.7834	1.40084	0.700420	+	0.713731i	$0.252996\pi$
$314$	−4.29674	−0.242479
$315$	2.85386	0.160797
$316$	3.44008	0.193520
$317$	−1.12233	−0.0630363	−0.0315181	−	0.999503i	$-0.510034\pi$
$317$	−1.12233	−0.0630363	−0.0315181	+	0.999503i	$0.510034\pi$
$318$	−2.23401	−0.125277
$319$	−2.73735	−0.153262
$320$	−7.81138	−0.436669
$321$	4.04038	0.225512
$322$	1.06459	0.0593274
$323$	16.1220	0.897053
$324$	−6.67842	−0.371023
$325$	−1.26172	−0.0699874
$326$	−11.3375	−0.627929
$327$	7.41358	0.409972
$328$	−4.18197	−0.230911
$329$	−0.960100	−0.0529321
$330$	−0.142850	−0.00786362
$331$	−20.9893	−1.15367	−0.576837	−	0.816859i	$-0.695713\pi$
$331$	−20.9893	−1.15367	−0.576837	+	0.816859i	$0.695713\pi$
$332$	9.97134	0.547248
$333$	20.6755	1.13301
$334$	−22.4477	−1.22828
$335$	−8.46038	−0.462240
$336$	−0.579409	−0.0316094
$337$	−9.41801	−0.513031	−0.256516	−	0.966540i	$-0.582575\pi$
$337$	−9.41801	−0.513031	−0.256516	+	0.966540i	$0.582575\pi$
$338$	−12.1449	−0.660598
$339$	4.48117	0.243384
$340$	−3.93695	−0.213511
$341$	0.650705	0.0352376
$342$	10.7824	0.583045
$343$	1.00000	0.0539949
$344$	−8.67308	−0.467621
$345$	−0.382286	−0.0205816
$346$	−12.5117	−0.672635
$347$	−3.76834	−0.202295	−0.101148	−	0.994871i	$-0.532251\pi$
$347$	−3.76834	−0.202295	−0.101148	+	0.994871i	$0.532251\pi$
$348$	2.58376	0.138504
$349$	−2.31376	−0.123853	−0.0619264	−	0.998081i	$-0.519724\pi$
$349$	−2.31376	−0.123853	−0.0619264	+	0.998081i	$0.519724\pi$
$350$	1.06459	0.0569049
$351$	2.82353	0.150709
$352$	1.57602	0.0840020
$353$	−34.2475	−1.82281	−0.911406	−	0.411507i	$-0.865002\pi$
$353$	−34.2475	−1.82281	−0.911406	+	0.411507i	$0.865002\pi$
$354$	1.34367	0.0714150
$355$	−3.58714	−0.190386
$356$	3.31571	0.175732
$357$	−1.73663	−0.0919124
$358$	0.956751	0.0505658
$359$	−14.2542	−0.752307	−0.376154	−	0.926557i	$-0.622754\pi$
$359$	−14.2542	−0.752307	−0.376154	+	0.926557i	$0.622754\pi$
$360$	−8.70942	−0.459027
$361$	−6.40496	−0.337103
$362$	−20.5955	−1.08248
$363$	−4.15805	−0.218241
$364$	1.09346	0.0573127
$365$	2.45676	0.128593
$366$	1.68632	0.0881455
$367$	30.3029	1.58180	0.790900	−	0.611945i	$-0.209613\pi$
$367$	30.3029	1.58180	0.790900	+	0.611945i	$0.209613\pi$
$368$	−1.51564	−0.0790083
$369$	−3.91071	−0.203584
$370$	7.71271	0.400965
$371$	−5.48925	−0.284987
$372$	−0.614194	−0.0318445
$373$	12.9356	0.669778	0.334889	−	0.942258i	$-0.391301\pi$
$373$	12.9356	0.669778	0.334889	+	0.942258i	$0.391301\pi$
$374$	−1.69750	−0.0877758
$375$	−0.382286	−0.0197412
$376$	2.93004	0.151105
$377$	9.83975	0.506773
$378$	−2.38240	−0.122537
$379$	−24.2479	−1.24553	−0.622765	−	0.782409i	$-0.713991\pi$
$379$	−24.2479	−1.24553	−0.622765	+	0.782409i	$0.713991\pi$
$380$	−3.07567	−0.157779
$381$	6.10032	0.312529
$382$	−9.90237	−0.506649
$383$	−27.1055	−1.38502	−0.692512	−	0.721406i	$-0.743496\pi$
$383$	−27.1055	−1.38502	−0.692512	+	0.721406i	$0.743496\pi$
$384$	−0.253917	−0.0129576
$385$	−0.351000	−0.0178886
$386$	−2.16147	−0.110016
$387$	−8.11052	−0.412281
$388$	13.5554	0.688173
$389$	23.4863	1.19080	0.595400	−	0.803429i	$-0.296994\pi$
$389$	23.4863	1.19080	0.595400	+	0.803429i	$0.296994\pi$
$390$	0.513492	0.0260017
$391$	−4.54276	−0.229737
$392$	−3.05181	−0.154139
$393$	−4.47998	−0.225985
$394$	14.8380	0.747526
$395$	3.96943	0.199724
$396$	0.868121	0.0436247
$397$	−24.7549	−1.24241	−0.621206	−	0.783647i	$-0.713357\pi$
$397$	−24.7549	−1.24241	−0.621206	+	0.783647i	$0.713357\pi$
$398$	−9.57548	−0.479975
$399$	−1.35671	−0.0679207
$400$	−1.51564	−0.0757821
$401$	−25.7078	−1.28378	−0.641892	−	0.766795i	$-0.721850\pi$
$401$	−25.7078	−1.28378	−0.641892	+	0.766795i	$0.721850\pi$
$402$	3.44320	0.171731
$403$	−2.33904	−0.116516
$404$	5.73478	0.285316
$405$	−7.70607	−0.382918
$406$	−8.30244	−0.412043
$407$	−2.54291	−0.126048
$408$	5.29987	0.262383
$409$	14.3339	0.708767	0.354384	−	0.935100i	$-0.384691\pi$
$409$	14.3339	0.708767	0.354384	+	0.935100i	$0.384691\pi$
$410$	−1.45884	−0.0720469
$411$	5.35528	0.264156
$412$	−9.23944	−0.455194
$413$	3.30156	0.162459
$414$	−3.03819	−0.149319
$415$	11.5057	0.564793
$416$	−5.66519	−0.277759
$417$	−3.12590	−0.153076
$418$	−1.32614	−0.0648638
$419$	−4.73137	−0.231142	−0.115571	−	0.993299i	$-0.536870\pi$
$419$	−4.73137	−0.231142	−0.115571	+	0.993299i	$0.536870\pi$
$420$	0.331306	0.0161661
$421$	12.2646	0.597741	0.298870	−	0.954294i	$-0.403390\pi$
$421$	12.2646	0.597741	0.298870	+	0.954294i	$0.403390\pi$
$422$	−0.938811	−0.0457006
$423$	2.73999	0.133223
$424$	16.7521	0.813555
$425$	−4.54276	−0.220356
$426$	1.45989	0.0707320
$427$	4.14351	0.200519
$428$	−9.15954	−0.442743
$429$	−0.169300	−0.00817389
$430$	−3.02552	−0.145903
$431$	−25.9042	−1.24776	−0.623882	−	0.781519i	$-0.714445\pi$
$431$	−25.9042	−1.24776	−0.623882	+	0.781519i	$0.714445\pi$
$432$	3.39178	0.163187
$433$	16.0090	0.769344	0.384672	−	0.923053i	$-0.374315\pi$
$433$	16.0090	0.769344	0.384672	+	0.923053i	$0.374315\pi$
$434$	1.97360	0.0947359
$435$	2.98134	0.142944
$436$	−16.8066	−0.804890
$437$	−3.54895	−0.169769
$438$	−0.999851	−0.0477747
$439$	−22.9093	−1.09340	−0.546701	−	0.837328i	$-0.684117\pi$
$439$	−22.9093	−1.09340	−0.546701	+	0.837328i	$0.684117\pi$
$440$	1.07119	0.0510668
$441$	−2.85386	−0.135898
$442$	6.10189	0.290237
$443$	−35.3107	−1.67766	−0.838830	−	0.544394i	$-0.816760\pi$
$443$	−35.3107	−1.67766	−0.838830	+	0.544394i	$0.816760\pi$
$444$	2.40023	0.113910
$445$	3.82592	0.181366
$446$	−6.07076	−0.287459
$447$	−4.02212	−0.190240
$448$	7.81138	0.369053
$449$	10.8135	0.510323	0.255161	−	0.966898i	$-0.417871\pi$
$449$	10.8135	0.510323	0.255161	+	0.966898i	$0.417871\pi$
$450$	−3.03819	−0.143222
$451$	0.480985	0.0226487
$452$	−10.1588	−0.477831
$453$	7.92404	0.372304
$454$	9.10140	0.427150
$455$	1.26172	0.0591501
$456$	4.14043	0.193893
$457$	14.4323	0.675117	0.337558	−	0.941305i	$-0.390399\pi$
$457$	14.4323	0.675117	0.337558	+	0.941305i	$0.390399\pi$
$458$	−14.7332	−0.688439
$459$	10.1660	0.474508
$460$	0.866643	0.0404075
$461$	−5.90665	−0.275100	−0.137550	−	0.990495i	$-0.543923\pi$
$461$	−5.90665	−0.275100	−0.137550	+	0.990495i	$0.543923\pi$
$462$	0.142850	0.00664597
$463$	32.3800	1.50483	0.752413	−	0.658692i	$-0.228890\pi$
$463$	32.3800	1.50483	0.752413	+	0.658692i	$0.228890\pi$
$464$	11.8201	0.548732
$465$	−0.708704	−0.0328654
$466$	−1.74844	−0.0809951
$467$	−19.6942	−0.911337	−0.455668	−	0.890150i	$-0.650600\pi$
$467$	−19.6942	−0.911337	−0.455668	+	0.890150i	$0.650600\pi$
$468$	−3.12057	−0.144248
$469$	8.46038	0.390664
$470$	1.02212	0.0471467
$471$	−1.54292	−0.0710942
$472$	−10.0757	−0.463773
$473$	0.997526	0.0458663
$474$	−1.61547	−0.0742012
$475$	−3.54895	−0.162837
$476$	3.93695	0.180450
$477$	15.6655	0.717275
$478$	−18.2696	−0.835630
$479$	31.0372	1.41812	0.709062	−	0.705146i	$-0.249119\pi$
$479$	31.0372	1.41812	0.709062	+	0.705146i	$0.249119\pi$
$480$	−1.71649	−0.0783468
$481$	9.14082	0.416786
$482$	20.7295	0.944204
$483$	0.382286	0.0173946
$484$	9.42630	0.428468
$485$	15.6413	0.710236
$486$	10.2834	0.466464
$487$	3.97996	0.180349	0.0901746	−	0.995926i	$-0.471257\pi$
$487$	3.97996	0.180349	0.0901746	+	0.995926i	$0.471257\pi$
$488$	−12.6452	−0.572421
$489$	−4.07122	−0.184107
$490$	−1.06459	−0.0480934
$491$	−22.9495	−1.03570	−0.517849	−	0.855472i	$-0.673267\pi$
$491$	−22.9495	−1.03570	−0.517849	+	0.855472i	$0.673267\pi$
$492$	−0.453997	−0.0204678
$493$	35.4276	1.59558
$494$	4.76699	0.214477
$495$	1.00171	0.0450233
$496$	−2.80979	−0.126163
$497$	3.58714	0.160905
$498$	−4.68258	−0.209831
$499$	−25.4986	−1.14147	−0.570737	−	0.821133i	$-0.693342\pi$
$499$	−25.4986	−1.14147	−0.570737	+	0.821133i	$0.693342\pi$
$500$	0.866643	0.0387575
$501$	−8.06078	−0.360129
$502$	1.97612	0.0881987
$503$	23.3437	1.04085	0.520423	−	0.853909i	$-0.325774\pi$
$503$	23.3437	1.04085	0.520423	+	0.853909i	$0.325774\pi$
$504$	8.70942	0.387948
$505$	6.61723	0.294463
$506$	0.373672	0.0166118
$507$	−4.36115	−0.193685
$508$	−13.8294	−0.613582
$509$	−21.2051	−0.939901	−0.469950	−	0.882693i	$-0.655728\pi$
$509$	−21.2051	−0.939901	−0.469950	+	0.882693i	$0.655728\pi$
$510$	1.84881	0.0818665
$511$	−2.45676	−0.108681
$512$	−16.0562	−0.709592
$513$	7.94201	0.350648
$514$	15.1673	0.669002
$515$	−10.6612	−0.469788
$516$	−0.941554	−0.0414496
$517$	−0.336996	−0.0148211
$518$	−7.71271	−0.338877
$519$	−4.49286	−0.197215
$520$	−3.85051	−0.168856
$521$	−30.5261	−1.33737	−0.668686	−	0.743545i	$-0.733143\pi$
$521$	−30.5261	−1.33737	−0.668686	+	0.743545i	$0.733143\pi$
$522$	23.6940	1.03706
$523$	27.6471	1.20892	0.604462	−	0.796634i	$-0.293388\pi$
$523$	27.6471	1.20892	0.604462	+	0.796634i	$0.293388\pi$
$524$	10.1561	0.443672
$525$	0.382286	0.0166843
$526$	−7.43409	−0.324142
$527$	−8.42162	−0.366852
$528$	−0.203373	−0.00885067
$529$	1.00000	0.0434783
$530$	5.84381	0.253839
$531$	−9.42219	−0.408888
$532$	3.07567	0.133347
$533$	−1.72896	−0.0748896
$534$	−1.55707	−0.0673809
$535$	−10.5690	−0.456937
$536$	−25.8194	−1.11523
$537$	0.343561	0.0148258
$538$	−9.07220	−0.391130
$539$	0.351000	0.0151187
$540$	−1.93942	−0.0834592
$541$	21.4769	0.923363	0.461681	−	0.887046i	$-0.347246\pi$
$541$	21.4769	0.923363	0.461681	+	0.887046i	$0.347246\pi$
$542$	−16.7840	−0.720935
$543$	−7.39569	−0.317379
$544$	−20.3973	−0.874527
$545$	−19.3928	−0.830694
$546$	−0.513492	−0.0219754
$547$	8.58072	0.366885	0.183443	−	0.983030i	$-0.441276\pi$
$547$	8.58072	0.366885	0.183443	+	0.983030i	$0.441276\pi$
$548$	−12.1404	−0.518613
$549$	−11.8250	−0.504678
$550$	0.373672	0.0159334
$551$	27.6772	1.17909
$552$	−1.16666	−0.0496565
$553$	−3.96943	−0.168797
$554$	5.56728	0.236531
$555$	2.76957	0.117562
$556$	7.08643	0.300531
$557$	−14.7364	−0.624401	−0.312200	−	0.950016i	$-0.601066\pi$
$557$	−14.7364	−0.624401	−0.312200	+	0.950016i	$0.601066\pi$
$558$	−5.63238	−0.238438
$559$	−3.58573	−0.151660
$560$	1.51564	0.0640476
$561$	−0.609559	−0.0257356
$562$	−15.1319	−0.638299
$563$	−40.9664	−1.72653	−0.863263	−	0.504754i	$-0.831583\pi$
$563$	−40.9664	−1.72653	−0.863263	+	0.504754i	$0.831583\pi$
$564$	0.318087	0.0133939
$565$	−11.7220	−0.493150
$566$	20.1043	0.845046
$567$	7.70607	0.323625
$568$	−10.9473	−0.459337
$569$	39.6846	1.66366	0.831832	−	0.555028i	$-0.187292\pi$
$569$	39.6846	1.66366	0.831832	+	0.555028i	$0.187292\pi$
$570$	1.44435	0.0604971
$571$	12.2920	0.514404	0.257202	−	0.966358i	$-0.417199\pi$
$571$	12.2920	0.514404	0.257202	+	0.966358i	$0.417199\pi$
$572$	0.383804	0.0160476
$573$	−3.55586	−0.148548
$574$	1.45884	0.0608907
$575$	1.00000	0.0417029
$576$	−22.2926	−0.928857
$577$	−19.6506	−0.818065	−0.409033	−	0.912520i	$-0.634134\pi$
$577$	−19.6506	−0.818065	−0.409033	+	0.912520i	$0.634134\pi$
$578$	3.87153	0.161035
$579$	−0.776167	−0.0322564
$580$	−6.75870	−0.280640
$581$	−11.5057	−0.477337
$582$	−6.36569	−0.263866
$583$	−1.92673	−0.0797969
$584$	7.49757	0.310252
$585$	−3.60076	−0.148873
$586$	21.3910	0.883654
$587$	−14.4020	−0.594433	−0.297216	−	0.954810i	$-0.596058\pi$
$587$	−14.4020	−0.594433	−0.297216	+	0.954810i	$0.596058\pi$
$588$	−0.331306	−0.0136628
$589$	−6.57925	−0.271093
$590$	−3.51482	−0.144703
$591$	5.32819	0.219172
$592$	10.9805	0.451294
$593$	−5.66020	−0.232436	−0.116218	−	0.993224i	$-0.537077\pi$
$593$	−5.66020	−0.232436	−0.116218	+	0.993224i	$0.537077\pi$
$594$	−0.836222	−0.0343106
$595$	4.54276	0.186235
$596$	9.11815	0.373494
$597$	−3.43847	−0.140727
$598$	−1.34321	−0.0549280
$599$	25.3733	1.03673	0.518363	−	0.855161i	$-0.326542\pi$
$599$	25.3733	1.03673	0.518363	+	0.855161i	$0.326542\pi$
$600$	−1.16666	−0.0476288
$601$	−15.4505	−0.630238	−0.315119	−	0.949052i	$-0.602044\pi$
$601$	−15.4505	−0.630238	−0.315119	+	0.949052i	$0.602044\pi$
$602$	3.02552	0.123311
$603$	−24.1447	−0.983249
$604$	−17.9638	−0.730937
$605$	10.8768	0.442205
$606$	−2.69307	−0.109399
$607$	33.4692	1.35847	0.679237	−	0.733919i	$-0.262311\pi$
$607$	33.4692	1.35847	0.679237	+	0.733919i	$0.262311\pi$
$608$	−15.9350	−0.646251
$609$	−2.98134	−0.120810
$610$	−4.41115	−0.178602
$611$	1.21137	0.0490069
$612$	−11.2355	−0.454168
$613$	13.7257	0.554376	0.277188	−	0.960816i	$-0.410597\pi$
$613$	13.7257	0.554376	0.277188	+	0.960816i	$0.410597\pi$
$614$	−3.51439	−0.141829
$615$	−0.523857	−0.0211239
$616$	−1.07119	−0.0431593
$617$	18.5285	0.745931	0.372965	−	0.927845i	$-0.378341\pi$
$617$	18.5285	0.745931	0.372965	+	0.927845i	$0.378341\pi$
$618$	4.33887	0.174535
$619$	13.6199	0.547430	0.273715	−	0.961811i	$-0.411748\pi$
$619$	13.6199	0.547430	0.273715	+	0.961811i	$0.411748\pi$
$620$	1.60663	0.0645239
$621$	−2.23785	−0.0898018
$622$	−30.5729	−1.22586
$623$	−3.82592	−0.153282
$624$	0.731050	0.0292654
$625$	1.00000	0.0400000
$626$	26.3842	1.05452
$627$	−0.476207	−0.0190179
$628$	3.49781	0.139578
$629$	32.9112	1.31225
$630$	3.03819	0.121045
$631$	31.8598	1.26832	0.634160	−	0.773202i	$-0.281346\pi$
$631$	31.8598	1.26832	0.634160	+	0.773202i	$0.281346\pi$
$632$	12.1139	0.481866
$633$	−0.337119	−0.0133993
$634$	−1.19482	−0.0474525
$635$	−15.9575	−0.633253
$636$	1.81862	0.0721129
$637$	−1.26172	−0.0499910
$638$	−2.91416	−0.115373
$639$	−10.2372	−0.404977
$640$	0.664206	0.0262551
$641$	−10.6682	−0.421369	−0.210685	−	0.977554i	$-0.567569\pi$
$641$	−10.6682	−0.421369	−0.210685	+	0.977554i	$0.567569\pi$
$642$	4.30136	0.169761
$643$	30.6440	1.20848	0.604240	−	0.796802i	$-0.293477\pi$
$643$	30.6440	1.20848	0.604240	+	0.796802i	$0.293477\pi$
$644$	−0.866643	−0.0341505
$645$	−1.08644	−0.0427785
$646$	17.1634	0.675284
$647$	1.39988	0.0550348	0.0275174	−	0.999621i	$-0.491240\pi$
$647$	1.39988	0.0550348	0.0275174	+	0.999621i	$0.491240\pi$
$648$	−23.5174	−0.923852
$649$	1.15885	0.0454888
$650$	−1.34321	−0.0526851
$651$	0.708704	0.0277763
$652$	9.22946	0.361453
$653$	−4.94921	−0.193678	−0.0968388	−	0.995300i	$-0.530873\pi$
$653$	−4.94921	−0.193678	−0.0968388	+	0.995300i	$0.530873\pi$
$654$	7.89244	0.308619
$655$	11.7189	0.457896
$656$	−2.07692	−0.0810903
$657$	7.01125	0.273535
$658$	−1.02212	−0.0398462
$659$	−16.7554	−0.652699	−0.326349	−	0.945249i	$-0.605819\pi$
$659$	−16.7554	−0.652699	−0.326349	+	0.945249i	$0.605819\pi$
$660$	0.116288	0.00452652
$661$	−23.3059	−0.906493	−0.453246	−	0.891385i	$-0.649734\pi$
$661$	−23.3059	−0.906493	−0.453246	+	0.891385i	$0.649734\pi$
$662$	−22.3450	−0.868463
$663$	2.19114	0.0850967
$664$	35.1132	1.36266
$665$	3.54895	0.137622
$666$	22.0110	0.852908
$667$	−7.79870	−0.301967
$668$	18.2738	0.707035
$669$	−2.17996	−0.0842821
$670$	−9.00686	−0.347965
$671$	1.45437	0.0561455
$672$	1.71649	0.0662151
$673$	38.7650	1.49428	0.747140	−	0.664667i	$-0.231427\pi$
$673$	38.7650	1.49428	0.747140	+	0.664667i	$0.231427\pi$
$674$	−10.0263	−0.386200
$675$	−2.23785	−0.0861348
$676$	9.88673	0.380259
$677$	−14.5851	−0.560551	−0.280275	−	0.959920i	$-0.590426\pi$
$677$	−14.5851	−0.560551	−0.280275	+	0.959920i	$0.590426\pi$
$678$	4.77062	0.183215
$679$	−15.6413	−0.600259
$680$	−13.8636	−0.531645
$681$	3.26824	0.125239
$682$	0.692735	0.0265262
$683$	−1.44892	−0.0554414	−0.0277207	−	0.999616i	$-0.508825\pi$
$683$	−1.44892	−0.0554414	−0.0277207	+	0.999616i	$0.508825\pi$
$684$	−8.77753	−0.335617
$685$	−14.0086	−0.535240
$686$	1.06459	0.0406463
$687$	−5.29058	−0.201848
$688$	−4.30738	−0.164217
$689$	6.92587	0.263854
$690$	−0.406979	−0.0154934
$691$	3.23800	0.123180	0.0615898	−	0.998102i	$-0.480383\pi$
$691$	3.23800	0.123180	0.0615898	+	0.998102i	$0.480383\pi$
$692$	10.1853	0.387188
$693$	−1.00171	−0.0380516
$694$	−4.01175	−0.152284
$695$	8.17686	0.310166
$696$	9.09846	0.344876
$697$	−6.22506	−0.235791
$698$	−2.46321	−0.0932340
$699$	−0.627852	−0.0237475
$700$	−0.866643	−0.0327560
$701$	32.2920	1.21965	0.609825	−	0.792536i	$-0.291240\pi$
$701$	32.2920	1.21965	0.609825	+	0.792536i	$0.291240\pi$
$702$	3.00591	0.113451
$703$	25.7113	0.969719
$704$	2.74180	0.103335
$705$	0.367033	0.0138233
$706$	−36.4597	−1.37218
$707$	−6.61723	−0.248867
$708$	−1.09383	−0.0411085
$709$	43.4228	1.63078	0.815388	−	0.578914i	$-0.196523\pi$
$709$	43.4228	1.63078	0.815388	+	0.578914i	$0.196523\pi$
$710$	−3.81885	−0.143319
$711$	11.3282	0.424840
$712$	11.6760	0.437575
$713$	1.85386	0.0694275
$714$	−1.84881	−0.0691898
$715$	0.442863	0.0165621
$716$	−0.778854	−0.0291071
$717$	−6.56044	−0.245004
$718$	−15.1749	−0.566322
$719$	−6.91933	−0.258047	−0.129024	−	0.991642i	$-0.541184\pi$
$719$	−6.91933	−0.258047	−0.129024	+	0.991642i	$0.541184\pi$
$720$	−4.32543	−0.161199
$721$	10.6612	0.397043
$722$	−6.81867	−0.253765
$723$	7.44379	0.276838
$724$	16.7660	0.623105
$725$	−7.79870	−0.289637
$726$	−4.42663	−0.164288
$727$	−16.7812	−0.622379	−0.311189	−	0.950348i	$-0.600727\pi$
$727$	−16.7812	−0.622379	−0.311189	+	0.950348i	$0.600727\pi$
$728$	3.85051	0.142709
$729$	−19.4255	−0.719464
$730$	2.61545	0.0968022
$731$	−12.9103	−0.477504
$732$	−1.37277	−0.0507390
$733$	20.9329	0.773173	0.386586	−	0.922253i	$-0.373654\pi$
$733$	20.9329	0.773173	0.386586	+	0.922253i	$0.373654\pi$
$734$	32.2603	1.19075
$735$	−0.382286	−0.0141008
$736$	4.49007	0.165506
$737$	2.96960	0.109387
$738$	−4.16332	−0.153254
$739$	18.0181	0.662805	0.331403	−	0.943489i	$-0.392478\pi$
$739$	18.0181	0.662805	0.331403	+	0.943489i	$0.392478\pi$
$740$	−6.27862	−0.230807
$741$	1.71179	0.0628841
$742$	−5.84381	−0.214533
$743$	−10.2450	−0.375852	−0.187926	−	0.982183i	$-0.560177\pi$
$743$	−10.2450	−0.375852	−0.187926	+	0.982183i	$0.560177\pi$
$744$	−2.16283	−0.0792931
$745$	10.5212	0.385468
$746$	13.7711	0.504196
$747$	32.8356	1.20139
$748$	1.38187	0.0505262
$749$	10.5690	0.386183
$750$	−0.406979	−0.0148608
$751$	−24.8429	−0.906532	−0.453266	−	0.891375i	$-0.649741\pi$
$751$	−24.8429	−0.906532	−0.453266	+	0.891375i	$0.649741\pi$
$752$	1.45517	0.0530646
$753$	0.709609	0.0258596
$754$	10.4753	0.381489
$755$	−20.7280	−0.754370
$756$	1.93942	0.0705359
$757$	14.8358	0.539215	0.269608	−	0.962970i	$-0.413106\pi$
$757$	14.8358	0.539215	0.269608	+	0.962970i	$0.413106\pi$
$758$	−25.8141	−0.937611
$759$	0.134183	0.00487052
$760$	−10.8307	−0.392871
$761$	25.4741	0.923435	0.461718	−	0.887027i	$-0.347233\pi$
$761$	25.4741	0.923435	0.461718	+	0.887027i	$0.347233\pi$
$762$	6.49435	0.235266
$763$	19.3928	0.702065
$764$	8.06114	0.291642
$765$	−12.9644	−0.468728
$766$	−28.8563	−1.04262
$767$	−4.16563	−0.150412
$768$	−6.24268	−0.225263
$769$	13.2780	0.478817	0.239409	−	0.970919i	$-0.423046\pi$
$769$	13.2780	0.478817	0.239409	+	0.970919i	$0.423046\pi$
$770$	−0.373672	−0.0134662
$771$	5.44646	0.196149
$772$	1.75957	0.0633284
$773$	51.0314	1.83547	0.917736	−	0.397191i	$-0.130015\pi$
$773$	51.0314	1.83547	0.917736	+	0.397191i	$0.130015\pi$
$774$	−8.63440	−0.310357
$775$	1.85386	0.0665925
$776$	47.7343	1.71356
$777$	−2.76957	−0.0993578
$778$	25.0033	0.896411
$779$	−4.86322	−0.174243
$780$	−0.418014	−0.0149673
$781$	1.25909	0.0450537
$782$	−4.83618	−0.172942
$783$	17.4523	0.623695
$784$	−1.51564	−0.0541301
$785$	4.03604	0.144053
$786$	−4.76935	−0.170117
$787$	−8.22391	−0.293151	−0.146575	−	0.989199i	$-0.546825\pi$
$787$	−8.22391	−0.293151	−0.146575	+	0.989199i	$0.546825\pi$
$788$	−12.0790	−0.430297
$789$	−2.66952	−0.0950374
$790$	4.22582	0.150348
$791$	11.7220	0.416788
$792$	3.05701	0.108626
$793$	−5.22793	−0.185649
$794$	−26.3539	−0.935263
$795$	2.09846	0.0744248
$796$	7.79503	0.276287
$797$	−22.2792	−0.789171	−0.394586	−	0.918859i	$-0.629112\pi$
$797$	−22.2792	−0.789171	−0.394586	+	0.918859i	$0.629112\pi$
$798$	−1.44435	−0.0511293
$799$	4.36150	0.154299
$800$	4.49007	0.158748
$801$	10.9186	0.385791
$802$	−27.3683	−0.966408
$803$	−0.862325	−0.0304308
$804$	−2.80297	−0.0988532
$805$	−1.00000	−0.0352454
$806$	−2.49012	−0.0877109
$807$	−3.25775	−0.114678
$808$	20.1945	0.710441
$809$	23.7593	0.835334	0.417667	−	0.908600i	$-0.362848\pi$
$809$	23.7593	0.835334	0.417667	+	0.908600i	$0.362848\pi$
$810$	−8.20383	−0.288253
$811$	−41.8480	−1.46948	−0.734741	−	0.678348i	$-0.762696\pi$
$811$	−41.8480	−1.46948	−0.734741	+	0.678348i	$0.762696\pi$
$812$	6.75870	0.237184
$813$	−6.02699	−0.211376
$814$	−2.70717	−0.0948861
$815$	10.6497	0.373041
$816$	2.63212	0.0921425
$817$	−10.0859	−0.352862
$818$	15.2598	0.533546
$819$	3.60076	0.125821
$820$	1.18758	0.0414722
$821$	−5.47664	−0.191136	−0.0955680	−	0.995423i	$-0.530467\pi$
$821$	−5.47664	−0.191136	−0.0955680	+	0.995423i	$0.530467\pi$
$822$	5.70119	0.198852
$823$	45.2620	1.57773	0.788867	−	0.614564i	$-0.210668\pi$
$823$	45.2620	1.57773	0.788867	+	0.614564i	$0.210668\pi$
$824$	−32.5358	−1.13344
$825$	0.134183	0.00467164
$826$	3.51482	0.122296
$827$	−49.6540	−1.72664	−0.863320	−	0.504657i	$-0.831619\pi$
$827$	−49.6540	−1.72664	−0.863320	+	0.504657i	$0.831619\pi$
$828$	2.47328	0.0859523
$829$	46.5612	1.61714	0.808568	−	0.588403i	$-0.200243\pi$
$829$	46.5612	1.61714	0.808568	+	0.588403i	$0.200243\pi$
$830$	12.2489	0.425165
$831$	1.99916	0.0693502
$832$	−9.85574	−0.341686
$833$	−4.54276	−0.157397
$834$	−3.32781	−0.115233
$835$	21.0857	0.729702
$836$	1.07956	0.0373375
$837$	−4.14865	−0.143398
$838$	−5.03697	−0.173999
$839$	27.2232	0.939848	0.469924	−	0.882707i	$-0.344281\pi$
$839$	27.2232	0.939848	0.469924	+	0.882707i	$0.344281\pi$
$840$	1.16666	0.0402537
$841$	31.8198	1.09723
$842$	13.0568	0.449968
$843$	−5.43372	−0.187147
$844$	0.764249	0.0263066
$845$	11.4081	0.392450
$846$	2.91697	0.100288
$847$	−10.8768	−0.373731
$848$	8.31974	0.285701
$849$	7.21928	0.247765
$850$	−4.83618	−0.165880
$851$	−7.24476	−0.248347
$852$	−1.18844	−0.0407153
$853$	23.2305	0.795398	0.397699	−	0.917516i	$-0.369809\pi$
$853$	23.2305	0.795398	0.397699	+	0.917516i	$0.369809\pi$
$854$	4.41115	0.150946
$855$	−10.1282	−0.346377
$856$	−32.2545	−1.10244
$857$	−34.9974	−1.19549	−0.597745	−	0.801687i	$-0.703936\pi$
$857$	−34.9974	−1.19549	−0.597745	+	0.801687i	$0.703936\pi$
$858$	−0.180236	−0.00615315
$859$	−5.36030	−0.182891	−0.0914455	−	0.995810i	$-0.529149\pi$
$859$	−5.36030	−0.182891	−0.0914455	+	0.995810i	$0.529149\pi$
$860$	2.46296	0.0839861
$861$	0.523857	0.0178530
$862$	−27.5775	−0.939292
$863$	32.9576	1.12189	0.560945	−	0.827853i	$-0.310438\pi$
$863$	32.9576	1.12189	0.560945	+	0.827853i	$0.310438\pi$
$864$	−10.0481	−0.341843
$865$	11.7526	0.399601
$866$	17.0431	0.579147
$867$	1.39024	0.0472149
$868$	−1.60663	−0.0545327
$869$	−1.39327	−0.0472635
$870$	3.17391	0.107606
$871$	−10.6746	−0.361695
$872$	−59.1829	−2.00419
$873$	44.6381	1.51077
$874$	−3.77818	−0.127799
$875$	−1.00000	−0.0338062
$876$	0.813940	0.0275005
$877$	4.59608	0.155199	0.0775993	−	0.996985i	$-0.475275\pi$
$877$	4.59608	0.155199	0.0775993	+	0.996985i	$0.475275\pi$
$878$	−24.3891	−0.823091
$879$	7.68133	0.259085
$880$	0.531991	0.0179334
$881$	21.4924	0.724097	0.362049	−	0.932159i	$-0.382077\pi$
$881$	21.4924	0.724097	0.362049	+	0.932159i	$0.382077\pi$
$882$	−3.03819	−0.102301
$883$	−25.9780	−0.874230	−0.437115	−	0.899406i	$-0.644000\pi$
$883$	−25.9780	−0.874230	−0.437115	+	0.899406i	$0.644000\pi$
$884$	−4.96731	−0.167069
$885$	−1.26214	−0.0424264
$886$	−37.5914	−1.26291
$887$	39.6189	1.33027	0.665136	−	0.746722i	$-0.268373\pi$
$887$	39.6189	1.33027	0.665136	+	0.746722i	$0.268373\pi$
$888$	8.45219	0.283637
$889$	15.9575	0.535196
$890$	4.07304	0.136529
$891$	2.70483	0.0906154
$892$	4.94197	0.165469
$893$	3.40735	0.114023
$894$	−4.28192	−0.143209
$895$	−0.898702	−0.0300403
$896$	−0.664206	−0.0221896
$897$	−0.482336	−0.0161047
$898$	11.5120	0.384161
$899$	−14.4577	−0.482191
$900$	2.47328	0.0824425
$901$	24.9363	0.830749
$902$	0.512053	0.0170495
$903$	1.08644	0.0361544
$904$	−35.7734	−1.18981
$905$	19.3459	0.643081
$906$	8.43587	0.280263
$907$	34.2063	1.13580	0.567900	−	0.823098i	$-0.307756\pi$
$907$	34.2063	1.13580	0.567900	+	0.823098i	$0.307756\pi$
$908$	−7.40909	−0.245879
$909$	18.8846	0.626364
$910$	1.34321	0.0445271
$911$	35.7670	1.18501	0.592507	−	0.805565i	$-0.298138\pi$
$911$	35.7670	1.18501	0.592507	+	0.805565i	$0.298138\pi$
$912$	2.05629	0.0680907
$913$	−4.03851	−0.133655
$914$	15.3646	0.508215
$915$	−1.58401	−0.0523657
$916$	11.9938	0.396285
$917$	−11.7189	−0.386992
$918$	10.8226	0.357201
$919$	−3.07030	−0.101280	−0.0506400	−	0.998717i	$-0.516126\pi$
$919$	−3.07030	−0.101280	−0.0506400	+	0.998717i	$0.516126\pi$
$920$	3.05181	0.100615
$921$	−1.26199	−0.0415839
$922$	−6.28818	−0.207090
$923$	−4.52595	−0.148974
$924$	−0.116288	−0.00382561
$925$	−7.24476	−0.238206
$926$	34.4715	1.13280
$927$	−30.4255	−0.999304
$928$	−35.0167	−1.14948
$929$	22.3675	0.733855	0.366928	−	0.930250i	$-0.380410\pi$
$929$	22.3675	0.733855	0.366928	+	0.930250i	$0.380410\pi$
$930$	−0.754481	−0.0247404
$931$	−3.54895	−0.116312
$932$	1.42334	0.0466231
$933$	−10.9785	−0.359419
$934$	−20.9662	−0.686037
$935$	1.59451	0.0521460
$936$	−10.9888	−0.359180
$937$	4.47289	0.146123	0.0730615	−	0.997327i	$-0.476723\pi$
$937$	4.47289	0.146123	0.0730615	+	0.997327i	$0.476723\pi$
$938$	9.00686	0.294084
$939$	9.47435	0.309184
$940$	−0.832065	−0.0271390
$941$	11.5898	0.377816	0.188908	−	0.981995i	$-0.439505\pi$
$941$	11.5898	0.377816	0.188908	+	0.981995i	$0.439505\pi$
$942$	−1.64258	−0.0535183
$943$	1.37033	0.0446240
$944$	−5.00399	−0.162866
$945$	2.23785	0.0727972
$946$	1.06196	0.0345272
$947$	−3.29463	−0.107061	−0.0535306	−	0.998566i	$-0.517047\pi$
$947$	−3.29463	−0.107061	−0.0535306	+	0.998566i	$0.517047\pi$
$948$	1.31509	0.0427123
$949$	3.09974	0.100622
$950$	−3.77818	−0.122580
$951$	−0.429051	−0.0139129
$952$	13.8636	0.449322
$953$	−18.1790	−0.588875	−0.294437	−	0.955671i	$-0.595132\pi$
$953$	−18.1790	−0.588875	−0.294437	+	0.955671i	$0.595132\pi$
$954$	16.6774	0.539951
$955$	9.30156	0.300991
$956$	14.8725	0.481012
$957$	−1.04645	−0.0338269
$958$	33.0419	1.06754
$959$	14.0086	0.452360
$960$	−2.98618	−0.0963786
$961$	−27.5632	−0.889136
$962$	9.73125	0.313748
$963$	−30.1624	−0.971969
$964$	−16.8751	−0.543510
$965$	2.03033	0.0653586
$966$	0.406979	0.0130943
$967$	−38.9229	−1.25168	−0.625839	−	0.779953i	$-0.715243\pi$
$967$	−38.9229	−1.25168	−0.625839	+	0.779953i	$0.715243\pi$
$968$	33.1939	1.06689
$969$	6.16322	0.197991
$970$	16.6516	0.534651
$971$	8.22331	0.263899	0.131949	−	0.991256i	$-0.457876\pi$
$971$	8.22331	0.263899	0.131949	+	0.991256i	$0.457876\pi$
$972$	−8.37132	−0.268510
$973$	−8.17686	−0.262138
$974$	4.23703	0.135763
$975$	−0.482336	−0.0154471
$976$	−6.28008	−0.201021
$977$	−26.4558	−0.846397	−0.423198	−	0.906037i	$-0.639093\pi$
$977$	−26.4558	−0.846397	−0.423198	+	0.906037i	$0.639093\pi$
$978$	−4.33419	−0.138592
$979$	−1.34290	−0.0429192
$980$	0.866643	0.0276839
$981$	−55.3442	−1.76700
$982$	−24.4319	−0.779653
$983$	39.5949	1.26288	0.631440	−	0.775424i	$-0.282464\pi$
$983$	39.5949	1.26288	0.631440	+	0.775424i	$0.282464\pi$
$984$	−1.59871	−0.0509650
$985$	−13.9377	−0.444092
$986$	37.7160	1.20112
$987$	−0.367033	−0.0116828
$988$	−3.88062	−0.123459
$989$	2.84195	0.0903688
$990$	1.06641	0.0338927
$991$	25.5200	0.810670	0.405335	−	0.914168i	$-0.367155\pi$
$991$	25.5200	0.810670	0.405335	+	0.914168i	$0.367155\pi$
$992$	8.32395	0.264286
$993$	−8.02391	−0.254631
$994$	3.81885	0.121126
$995$	8.99450	0.285145
$996$	3.81191	0.120785
$997$	−11.2789	−0.357205	−0.178603	−	0.983921i	$-0.557158\pi$
$997$	−11.2789	−0.357205	−0.178603	+	0.983921i	$0.557158\pi$
$998$	−27.1456	−0.859279
$999$	16.2127	0.512946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.a.l.1.4	✓	5
3.2	odd	2		7245.2.a.bh.1.2		5
5.4	even	2		4025.2.a.q.1.2		5
7.6	odd	2		5635.2.a.y.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.l.1.4	✓	5	1.1	even	1	trivial
4025.2.a.q.1.2		5	5.4	even	2
5635.2.a.y.1.4		5	7.6	odd	2
7245.2.a.bh.1.2		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.a (trivial)

\(f(q)\)	\(=\)	\(q+1.06459 q^{2} +0.382286 q^{3} -0.866643 q^{4} -1.00000 q^{5} +0.406979 q^{6} +1.00000 q^{7} -3.05181 q^{8} -2.85386 q^{9} +O(q^{10})\)	\(q+1.06459 q^{2} +0.382286 q^{3} -0.866643 q^{4} -1.00000 q^{5} +0.406979 q^{6} +1.00000 q^{7} -3.05181 q^{8} -2.85386 q^{9} -1.06459 q^{10} +0.351000 q^{11} -0.331306 q^{12} -1.26172 q^{13} +1.06459 q^{14} -0.382286 q^{15} -1.51564 q^{16} -4.54276 q^{17} -3.03819 q^{18} -3.54895 q^{19} +0.866643 q^{20} +0.382286 q^{21} +0.373672 q^{22} +1.00000 q^{23} -1.16666 q^{24} +1.00000 q^{25} -1.34321 q^{26} -2.23785 q^{27} -0.866643 q^{28} -7.79870 q^{29} -0.406979 q^{30} +1.85386 q^{31} +4.49007 q^{32} +0.134183 q^{33} -4.83618 q^{34} -1.00000 q^{35} +2.47328 q^{36} -7.24476 q^{37} -3.77818 q^{38} -0.482336 q^{39} +3.05181 q^{40} +1.37033 q^{41} +0.406979 q^{42} +2.84195 q^{43} -0.304192 q^{44} +2.85386 q^{45} +1.06459 q^{46} -0.960100 q^{47} -0.579409 q^{48} +1.00000 q^{49} +1.06459 q^{50} -1.73663 q^{51} +1.09346 q^{52} -5.48925 q^{53} -2.38240 q^{54} -0.351000 q^{55} -3.05181 q^{56} -1.35671 q^{57} -8.30244 q^{58} +3.30156 q^{59} +0.331306 q^{60} +4.14351 q^{61} +1.97360 q^{62} -2.85386 q^{63} +7.81138 q^{64} +1.26172 q^{65} +0.142850 q^{66} +8.46038 q^{67} +3.93695 q^{68} +0.382286 q^{69} -1.06459 q^{70} +3.58714 q^{71} +8.70942 q^{72} -2.45676 q^{73} -7.71271 q^{74} +0.382286 q^{75} +3.07567 q^{76} +0.351000 q^{77} -0.513492 q^{78} -3.96943 q^{79} +1.51564 q^{80} +7.70607 q^{81} +1.45884 q^{82} -11.5057 q^{83} -0.331306 q^{84} +4.54276 q^{85} +3.02552 q^{86} -2.98134 q^{87} -1.07119 q^{88} -3.82592 q^{89} +3.03819 q^{90} -1.26172 q^{91} -0.866643 q^{92} +0.708704 q^{93} -1.02212 q^{94} +3.54895 q^{95} +1.71649 q^{96} -15.6413 q^{97} +1.06459 q^{98} -1.00171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} + q^{10} - 7 q^{11} - 10 q^{12} - 5 q^{13} - q^{14} + 4 q^{15} - 9 q^{16} - 7 q^{17} + 11 q^{18} - 10 q^{19} - 3 q^{20} - 4 q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} + 5 q^{25} - 2 q^{26} - 7 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 10 q^{31} + 4 q^{33} - 10 q^{34} - 5 q^{35} + 20 q^{36} - 3 q^{37} - 15 q^{38} - 13 q^{39} - 3 q^{40} - 15 q^{41} - 5 q^{42} + 8 q^{43} - 27 q^{44} - 5 q^{45} - q^{46} - 10 q^{47} - 2 q^{48} + 5 q^{49} - q^{50} - 18 q^{51} + 18 q^{52} - 9 q^{53} - 39 q^{54} + 7 q^{55} + 3 q^{56} + 23 q^{57} - 31 q^{58} - 19 q^{59} + 10 q^{60} - 21 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} + 5 q^{65} + 25 q^{66} + 5 q^{67} - 15 q^{68} - 4 q^{69} + q^{70} - 16 q^{71} + 26 q^{72} + q^{73} - 16 q^{74} - 4 q^{75} - 7 q^{77} + 28 q^{78} + 20 q^{79} + 9 q^{80} - 3 q^{81} + 11 q^{82} - 31 q^{83} - 10 q^{84} + 7 q^{85} + 10 q^{86} + 38 q^{87} - 3 q^{88} - 21 q^{89} - 11 q^{90} - 5 q^{91} + 3 q^{92} + 23 q^{93} + 28 q^{94} + 10 q^{95} + 24 q^{96} + 19 q^{97} - q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 + q^10 - 7 * q^11 - 10 * q^12 - 5 * q^13 - q^14 + 4 * q^15 - 9 * q^16 - 7 * q^17 + 11 * q^18 - 10 * q^19 - 3 * q^20 - 4 * q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 + 5 * q^25 - 2 * q^26 - 7 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 10 * q^31 + 4 * q^33 - 10 * q^34 - 5 * q^35 + 20 * q^36 - 3 * q^37 - 15 * q^38 - 13 * q^39 - 3 * q^40 - 15 * q^41 - 5 * q^42 + 8 * q^43 - 27 * q^44 - 5 * q^45 - q^46 - 10 * q^47 - 2 * q^48 + 5 * q^49 - q^50 - 18 * q^51 + 18 * q^52 - 9 * q^53 - 39 * q^54 + 7 * q^55 + 3 * q^56 + 23 * q^57 - 31 * q^58 - 19 * q^59 + 10 * q^60 - 21 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 + 5 * q^65 + 25 * q^66 + 5 * q^67 - 15 * q^68 - 4 * q^69 + q^70 - 16 * q^71 + 26 * q^72 + q^73 - 16 * q^74 - 4 * q^75 - 7 * q^77 + 28 * q^78 + 20 * q^79 + 9 * q^80 - 3 * q^81 + 11 * q^82 - 31 * q^83 - 10 * q^84 + 7 * q^85 + 10 * q^86 + 38 * q^87 - 3 * q^88 - 21 * q^89 - 11 * q^90 - 5 * q^91 + 3 * q^92 + 23 * q^93 + 28 * q^94 + 10 * q^95 + 24 * q^96 + 19 * q^97 - q^98 - 26 * q^99

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